Question

3. The CO2 asymmetric stretching occurs at 2350 cm1. Calculate the energy needed for the first overtone transition, and describe how the energy would change if anharmonicity is taken into account.

Answer 1

As per the question, wave number corresponding to the fundamental band =2350 cm ^-1

Fundamental is corresponding to the selection rule, Δv =±1

The first overtone band corresponds to the transition in accordance with the selection rule Δv=±2 (anharmonic oscillator).

The energy band position corresponding to the first overtone ~ 2 x position of the fundamental band (cm^-1)

:. As per the data given in the problem energy corresponding to the first overtone ~2 x 2350 cm^-1

                                                                                                                                           ⁼4700 cm^-1

When we consider anharmonicity in to account,

Equation for fundamental band is given as   ΔE=_e (1-2x_e)cm^-1

Equationfor fundamental band is given as   ΔE=2_e (1-3x_e)cm^-1

Where   _e= equilibrium oscillation frequency

And         x_e=anharmonicity constant

Using these equations we can calculate the precise energy values taking anharmonicity constant and equilibrium oscillation frequency (or wave number) in to account(provided those values are available for the given molecular system).